where \(R\)  is the usual Ricci scalar and \(\mathcal {S}_{4}^{(i)}\)  are called quasi-topological Lagrangian densities [1]}.
Clearly there are six such quartic curvature combinations that are nontrivial in (3+1) dimensions, leading to the introduction of six dimension-independent new coupling constants. Under the imposition of spherical symmetry
the field equations differ by terms that vanish for a static spherically symmetric (SSS) metric, leading to a
degeneracy that yields one new effective coupling constant that is a linear combination of the six couplings. We shall henceforth only consider this case.
